This is the official press release sent out announcing their civil restructuring. There's a lot of legal speak in it, but further down one of the important sections is their outlook for the situation. It states that the game division is clearly the most desirable and functional part of Index's business, and that's one area they plan on expanding on specifically. They will seek out and select a sponsor as soon as possible to conduct a business transfer before the situation further damages the value of this core business.

All that will happen is that they'll undergo "reorganization" and then it'll be business as usual. Japanese bankruptcy laws are Neat Like That. Whether or not this will have an actual impact on Atlus is unknown, but it is unlikely.

...well, I guess they might start pumping out Persona games on a yearly basis.

To quote a market research firm's English-language FAQ about the procedure...

Originally Posted by Teikoku Databank

Civil Rehabilitation Law
The Civil Rehabilitation Law was introduced in April 2000, replacing the Composition Law. The Civil Rehabilitation Law may be applied to all corporations and individuals, including joint stock companies, limited liability companies, medical corporations and educational corporations. The purpose of the Civil Rehabilitation Law is rapid rehabilitation before a corporate failure becomes more serious. The party applying the Law is normally an obligor. A creditor may also apply, however. The management rights rest with the former management in principle. However, there are cases in which a supervision order (supervision committee members are selected and given guardianship over a business owner) or an administration order (an administrator is selected and appointed and manages the business in place of the business owner) may be issued based on an application of an interested person or the official power of a court. The approval of a rehabilitation plan requires the approval of a majority of creditors present owed half or more of the amount of reported credits. If the approval of creditors with three fifths or more of reported credits is obtained, a procedure to investigate and determine credits may be omitted (simple rehabilitation). If approved by all of notified creditors, approval for a plan can be obtained immediately (approved rehabilitation).

The tl;dr is that it's definitely a reorganization, rather than liquidation or absorption. Index will continue operating, under the ownership of some combination of current management and current creditors. Think, say, GM or Chrysler.